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CAT 2018 Question Paper | Quants Slot 2

CAT Previous Year Paper | CAT Set Theory Questions | Question 31

A very simple problem from Set Theory that appered in the CAT 2018 Question Paper. In CAT Previous year paper we come across some questions that are very taxing and here we are, having a look at one of the simplest questions of the paper. The CAT Previous Year paper is by far the best place to kick start your CAT Online Preparation. To have a look at more CAT-level questions, visit 2IIM's CAT Question Bank

Question 31 : For two sets A and B, let A △ B denote the set of elements which belong to A or B but not both. If P = {1,2,3,4}, Q = {2,3,5,6,}, R = {1,3,7,8,9}, S = {2,4,9,10}, then the number of elements in (P △ Q) △ (R △ S) is

  1. 7
  2. 8
  3. 9
  4. 6

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Explanatory Answer

Method of solving this CAT Question from Set Theory
CAT 2018 Question Paper Quants Slot 2 Set Theory

Given that for two sets A and B, A △ B denote the set of elements which belong to A or B but not both.
This is the diagram which represents A △ B ,the set of elements which belongs to A or B i.e. A intersection B subtracted from A union B
We have to find the number of elements in (P △ Q) △ (R △ S) if
P = {1 , 2 , 3 , 4} Q = {2 , 3 , 5 , 6 ,} R = {1 , 3 , 7 , 8 , 9} S = {2 , 4 , 9 , 10}
For P △ Q, we have to find the elements which do not to belong to both P and Q such that
(P △ Q) = {1, 4 , 5 , 6}
(R △ S) = {1 , 2 , 3 , 4 , 7 , 8 , 10}
(P △ Q) △ (R △ S) = {2 , 3 , 5 , 7 , 6 , 8 , 10}
The number of elements (P △ Q) △ (R △ S) is 7

The question is "For two sets A and B, let A △ B denote the set of elements which belong to A or B but not both. If P = {1,2,3,4}, Q = {2,3,5,6,}, R = {1,3,7,8,9}, S = {2,4,9,10}, then the number of elements in (P △ Q) △ (R △ S) is"

Hence, the answer is 7

Choice A is the correct answer

 

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